Aircraft: EMB ERJ 170/175 ER/LR
Phase of flight: Parked
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown

When we arrived at the aircraft; the interior was extremely warm due to the external air having not yet been connected. As soon as we arrived at the aircraft; the Captain had the First Officer tell the ramp agents to connect the external air as soon as possible; so that the cabin could be supplied with cool air to create a comfortable cabin temperature appropriate for boarding. Additionally; since this flight was scheduled to depart after XA00 local; it was not considered a STAR flight so we could save some fuel by not starting the APU as soon as possible (as is the procedure with STAR flights); and instead start the APU by D-12. The ramp agents promptly connected external air to the aircraft within about 4 minutes of the request; and the cabin was at an appropriate temperature by about D-35. However; as the passengers boarded; the internal cabin temperature once again began to creep up; so we started the APU at about D-20. After the APU was up and running; intending to signal to them to disconnect both the GPU and external air; we looked out the window for any ramp agents and pressed the horn to get their attention; but no one was available in front of the aircraft; since they were probably all occupied below the aircraft; loading bags.Finally; after the load closeout report was received from CLP; we communicated to the flight attendants that we were ready for door closure and were also able to get the attention of a ramp agent; and we exchanged hand signals to disconnect both the GPU and external air. Once the aircraft was all closed up; we had our headsets on and all checklists were complete; we attempted to call the ramp agents over the ramp interphone system; but we received no response as there was no one on the ramp headset. We observed the jetway move away from the aircraft; then inexplicably move back towards the aircraft. We signaled to the ramp agents to put their headset on so that we could get some perspective about what was going on; but the ramp agents signaled that they were having trouble with their headset. We then called the Station to ask what was going on; and they indicated something went wrong with ramp procedures; there may be some damage; and we should prepare for the jetway agent to open the aircraft up again. We then called the flight attendants and told them to prepare to open the aircraft up again. We ran the Parking Checklist and opened the flightdeck door; then made a PA to the pax about what was happening.We soon heard that the PCA hose had still been connected between the jetway and aircraft while the jetway was moved rearward; which caused the aircraft's external air intake manifold (which accepts air from a hose connected to the jetway) to be ripped from the aircraft by the rearward movement of the jetway. This dislocated manifold component had fallen out from the bottom of the aircraft. We did not hear or feel anything (no 'pop' or jolt) while this was happening.After door opening procedures were complete and we made all appropriate communications; we went out and saw the fallen manifold component laying forlornly on the tarmac below the PCA intake hatch. We then called maintenance for aircraft inspection.After the APU was up and running; but we could not get anyone's attention to connect the power and the air; we should have been more proactive to go outside and track someone down to disconnect the power or to call Station to get someone to disconnect the ground power cord and external air hose. However; we were occupied at this time; being engaged in our preflight briefing procedures and before-start checklist.Since ramp Ops are so important to a successful; safe and on-time departure of an aircraft; we should ALWAYS have at least one ramp agent with 'eyes on' the flight deck at ALL TIMES. This is important because external accessories such as GPU and/or external air/PCA need to be connected and/or disconnected in a timely fashion. In this case; if the external air hosehad been disconnected in a timely fashion; it would have eliminated the risk of the incident which occurred. We can accomplish 'eyes on' in one or more of the following ways:1. Physically position a ramp agent at the nose of the aircraft throughout the turn to supervise ramp procedures and watch for hand signals from the flight deck.2. Install mirrors at each and every gate in the system; angled in such a way so that signals from the flight deck can be seen by ramp agents working underneath the right-hand side of the aircraft.3. Emphasize during ramp agent training that when the E175 horn sounds; that means the pilots in the flight deck need to get the attention of a ramp agent; and they should immediately walk over to the nose of the aircraft to look for hand signals from the flight deck. In this incident; we sounded the horn several times with no one walking to the front of the aircraft... they just kept working.It is important that the jetway driver positively confirm- both visually and by hand signals from rampers- that ALL jetway-connected external accessory hoses/cords are disconnected from the aircraft PRIOR to jetway movement. It is also important that ramp agents give the jetway driver and other rampers correct hand signals which can be clearly interpreted.It would also be nice if ramp agents were provided with reliable headsets at all stations. While we do have hand signals we use to communicate visually with ramp agents; and while this may not have prevented this particular incident; the inability to accomplish effectively communication with ramp agents in a timely fashion is a continuing frustration. E175 Captain reported the aircraft was damaged when the jetway was pulled away with the external air conditioning hose still attached.